Question

Find the sum of all four digit numbers which are divisible by 7.
a)7071071
b)9872134
c)8105013
d)1019996
Find which is the correct answer and Explain it?

Answer 1

Answer:

7071071

option (a) is correct

Step-by-step explanation:

The four digit numbers which are divisible by 7 are

1001,1008,1015................9996

This is an A.P with common difference ,d=7 and first term, a=1001

Number of terms in the A.P

$\bf{n=\frac{l-a}{d}+1}$

$n=\frac{9996-1001}{7}+1$

$n=\frac{8995}{7}+1$

$n=1285+1$

$n=1286$

Sum of four digit numbers which are divisible by 7

$\bf{S_n=\frac{n}{2}[2a+(n-1)d]}$

$S_{1286}=\frac{1286}{2}[2(1001)+(1286-1)7]$

$S_{1286}=643[2002+(1285)7]$

$S_{1286}=643[2002+8995]$

$S_{1286}=643[10997]$

$\implies\:\bf{S_{1286}=7071071}$